# Luis Santal\'o and classical field theory

## TL;DR

This paper reviews Luis Santaló's contributions to integral geometry, number theory, differential equations, stochastic geometry, functional analysis, and his work on general relativity and unified field theories, highlighting his classification theorem for tensors.

## Contribution

It provides a comprehensive overview of Santaló's work in theoretical physics, especially his classification of tensors in generalized Einstein theories.

## Key findings

- Santaló's classification theorem for tensors in generalized relativity.
- His work connects integral geometry with theoretical physics.
- Historical insights into Santaló's influence on modern mathematics and physics.

## Abstract

Considered one of the founding fathers of integral geometry, Luis Santal\'o has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950's and the 1970's, he wrote a series of papers on general relativity and on the attempts at generalizing Einstein's theory to formulate a unified field theory. His main contribution in this subject was to provide a classification theorem for the plethora of tensors that were populating Einstein's generalized theory. This paper, which is the transcript of the conferences delivered by the authors in occasion of the celebration of the 100th anniversary of Luis Santal\'o's birth, revisits his work on theoretical physics.